Modelling repayment patterns in the collections process for unsecured consumer debt: A case study

• We use Markov chain models of payment patterns to estimate recovery rates.
• Models allow optimisation of write off policies.
• Models tested using large portfolio of UK retail loans during a 12 year period.
• Results aid the management of collections particularly the write-off decision.

One approach to modelling Loss Given Default (LGD), the percentage of the defaulted amount of a loan that a lender will eventually lose is to model the collections process. This is particularly relevant for unsecured consumer loans where LGD depends both on a defaulter's ability and willingness to repay and the lender's collection strategy. When repaying such defaulted loans, defaulters tend to oscillate between repayment sequences where the borrower is repaying every period and non-repayment sequences where the borrower is not repaying in any period. This paper develops two models – one a Markov chain approach and the other a hazard rate approach to model such payment patterns of debtors. It also looks at simplifications of the models where one assumes that after a few repayment and non-repayment sequences the parameters of the model are fixed for the remaining payment and non-payment sequences. One advantage of these approaches is that they show the impact of different write-off strategies. The models are applied to a real case study and the LGD for that portfolio is calculated under different write-off strategies and compared with the actual LGD results.